Modeling and Multivariate Methods - SAS

Chapter 3 Fitting Standard Least Squares Models 87
Effect Screening
The resulting posterior probabilities are listed and plotted with bars as shown in Figure 3.25. An overall
posterior probability is also shown for the outcome that the sample is uncontaminated.
Bayes Plot for Factor Activity
JMP includes a script that helps you determine which factors are active in the design.
1. Open the Reactor.jmp sample data table.
1. Open the BayesPlotforFactors.jsl file in the Sample Scripts folder.
2. Select Edit > Run Script.
3. Select Y and click Y, Response.
4. Select F, Ct, A, T, and Cn and click X, Factor.
5. Click OK.
Figure 3.26 Bayes Plot for Factor Activity
In this case, we specified that the highest order interaction to consider is two. Therefore, all possible models
that include (up to) second-order interactions are constructed. Based on the value assigned to Prior
Probability (see the Controls section of the plot), a posterior probability is computed for each of the possible
models. The probability for a factor is the sum of the probabilities for each of the models where it was
involved.
In this example, we see that Ct, T, and Cn are active and that A and F are not. These results match those of
the Bayes Plot shown in Figure 3.25.
Note: If the ridge parameter were zero (not allowed), all the models would be fit by least squares. As the
ridge parameter gets large, the parameter estimates for any model shrink toward zero. Details on the ridge
parameter (and why it cannot be zero) are explained in Box and Meyer (1993).